How do you explain factors?
In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.
Properties of Factors
- Each number is a factor of itself. Eg. 72 and 84 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 72 and also of 84.
- Every number is a factor of zero (0), since 72 x 0 = 0 and 84 x 0 = 0.
- Every number other than 1 has at least two factors, namely the number itself and 1.
- Every factor of a number is an exact divisor of that number, example 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 are exact divisors of 72 and 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 are exact divisors of 84.
- Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Each factor divides 72 without leaving a remainder.
Simlarly, factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. Each factor divides 84 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 are all less than or equal to 72 and 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 are all less than or equal to 84.
Steps to find Factors of 72 and 84
- Step 1. Find all the numbers that would divide 72 and 84 without leaving any remainder. Starting with the number 1 upto 36 (half of 72) and 1 upto 42 (half of 84). The number 1 and the number itself are always factors of the given number.
72 ÷ 1 : Remainder = 0
84 ÷ 1 : Remainder = 0
72 ÷ 2 : Remainder = 0
84 ÷ 2 : Remainder = 0
72 ÷ 3 : Remainder = 0
84 ÷ 3 : Remainder = 0
72 ÷ 4 : Remainder = 0
84 ÷ 4 : Remainder = 0
72 ÷ 6 : Remainder = 0
84 ÷ 6 : Remainder = 0
72 ÷ 8 : Remainder = 0
84 ÷ 7 : Remainder = 0
72 ÷ 9 : Remainder = 0
84 ÷ 12 : Remainder = 0
72 ÷ 12 : Remainder = 0
84 ÷ 14 : Remainder = 0
72 ÷ 18 : Remainder = 0
84 ÷ 21 : Remainder = 0
72 ÷ 24 : Remainder = 0
84 ÷ 28 : Remainder = 0
72 ÷ 36 : Remainder = 0
84 ÷ 42 : Remainder = 0
72 ÷ 72 : Remainder = 0
84 ÷ 84 : Remainder = 0
Hence, Factors of
72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72
And, Factors of
84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84
Examples of GCF
Sammy baked 72 chocolate cookies and 84 fruit and nut cookies to package in plastic containers for her friends at college. She wants to divide the cookies into identical boxes so that each box has the same number of each kind of cookies. She wishes that each box should have greatest number of cookies possible, how many plastic boxes does she need?Since Sammy wants to pack greatest number of cookies possible. So for calculating total number of boxes required we need to calculate the GCF of 72 and 84.
GCF of 72 and 84 is 12.
What is the difference between GCF and LCM?Major and simple difference betwen GCF and LCM is that GCF gives you the greatest common factor while LCM finds out the least common factor possible for the given numbers.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(72, 84) = ( 72 * 84 ) / LCM(72, 84) = 12.
What is the GCF of 72 and 84?GCF of 72 and 84 is 12.
Ram has 72 cans of Pepsi and 84 cans of Coca Cola. He wants to create identical refreshment tables that will be organized in his house warming party. He also doesn't want to have any can left over. What is the greatest number of tables that Ram can arrange?To find the greatest number of tables that Ram can stock we need to find the GCF of 72 and 84. Hence GCF of 72 and 84 is 12. So the number of tables that can be arranged is 12.
Rubel is creating individual servings of starters for her birthday party. He has 72 pizzas and 84 hamburgers. He wants each serving to be identical, with no left overs. Can you help Rubel in arranging the same in greatest possible way?The greatest number of servings Rubel can create would be equal to the GCF of 72 and 84. Thus GCF of 72 and 84 is 12.
Ariel is making ready to eat meals to share with friends. She has 72 bottles of water and 84 cans of food, which she would like to distribute equally, with no left overs. What is the greatest number of boxes Ariel can make?The greatest number of boxes Ariel can make would be equal to GCF of 72 and 84. So the GCF of 72 and 84 is 12.
Mary has 72 blue buttons and 84 white buttons. She wants to place them in identical groups without any buttons left, in the greatest way possible. Can you help Mary arranging them in groups?Greatest possible way in which Mary can arrange them in groups would be GCF of 72 and 84. Hence, the GCF of 72 and 84 or the greatest arrangement is 12.
Kamal is making identical balloon arrangements for a party. He has 72 maroon balloons, and 84 orange balloons. He wants each arrangement tohave the same number of each color. What is the greatest number of arrangements that he can make if every balloon is used?The greatest number of arrangements that he can make if every balloon is used would be equal to GCF of 72 and 84. So the GCF of 72 and 84 is 12.